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Recurrent configurations form a finite abelian group, and repeated grain addition at a specific site generates deterministic dynamics on this group. Using Dhar's formulation, the sandpile group is identified with the co-kernel of the reduced directed Laplacian. We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition.","authors_text":"Abdul Quadir, Nikita Kalinin, Ram Ramaswamy","cross_cats":[],"headline":"The sandpile group on a directed cylindrical lattice reduces exactly to a transverse problem.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T12:52:20Z","title":"The Directed Abelian Sandpile Model on Cylinders"},"references":{"count":14,"internal_anchors":1,"resolved_work":14,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"In particu- lar, odd and even transverse widths lead to qualitatively different algebraic structures","work_id":"298fbb2a-1557-4cb2-9530-aeadc9434777","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"The directed ladder [8, 9] is a special limit of the cylin- drical construction","work_id":"e8e427ac-d27f-4bb4-a615-b866cbc5b1bd","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"P. 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